Mixing processes with different stirring systems in agitated vessels are simulated by a multi-region model. Because of discontinuities at the boundaries of different regions appearing for the already-existing simple three-region model, unrealistic values occur during the calculation of the concentration distribution at these locations. Therefore, the region model will be modified at first. The procedure is presented here for the example of a radial flow stirrer, considering the fluid velocity, the turbulence field, the particle diffusion, and the relative fluid-to-particle velocity. The modified model is discussed and validated. Thus, the behavior of single particles and particle swarms can be analyzed in the vessel considering different aspects.
Modeling of the Laminar Flow in the Entrance Region of Tubes and Ducts and its Impact on the Residence Time DistributionA one-range and a two-range model for the laminar velocity distribution in the entrance region of tubes and ducts are presented. These allow the calculation of the residence time distribution under the impact of the flow development in the hydrodynamic entrance region. For the dispersion-free case, an analytical solution is given. A cell model with place-changing probability (ZEMP) is applied for the consideration of dispersion. This approach allows the fast quantification of the influence of different parameters on the residence time distribution for relatively short pipes and ducts. The numerical results are compared with earlier presented results of semi-empirical models.
Mixing processes in agitated vessels with different stirring systems are simulated using a cell model. The model takes the fluid velocity and fluid turbulence, as well as the diffusion and the sedimentation velocity of the particles into account. The two-and three-dimensional behaviors of single particles and collectives of particles in the vessels, respectively, are discussed in terms of different aspects. The calculated concentration distributions are compared with some measurements from the literature. Furthermore, a user interface developed for the calculation program, is introduced. , it is possible to connect both models using an advanced velocity model. However, these connections are not applied for the calculation of the axial flow impeller presented here.The tangential velocity at the exterior of the stirrer jet stream does not depend on the axial direction for the unbaffled case b and for the calculation model used here 1) . The model results in a tangential velocity being totally locally independent for the cases c 1 and c 2 , Fig. 3.
Conditions of Mass AdditionThe temporal progress of mixing processes strongly depends on the location of the addition [5]. In order to solve problems that are relevant in practice, different possibilities of addition can be chosen in the program. In general, particles having a density different from the fluid are added with a volume fraction of 60 %, for the calculation of collectives of particles following the value of closely packed spheres, if no other value is defined. The volume of the substance added should not affect the filling level.
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